Find each product. See Examples 3–5. (3w+2)(-w^2+4w-3)

Key Concepts

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process, often referred to as the distributive property, requires careful attention to combine like terms and ensure all products are accounted for. For example, in the expression (3w + 2)(-w^2 + 4w - 3), each term in the first polynomial must be multiplied by each term in the second.

Combining Like Terms

Combining like terms is a fundamental algebraic process where terms with the same variable and exponent are added or subtracted to simplify an expression. This step is crucial after multiplying polynomials, as it helps to condense the expression into its simplest form. For instance, after multiplying the polynomials, you may end up with several terms that can be combined based on their variable parts.

Standard Form of a Polynomial

The standard form of a polynomial is a way of writing the polynomial such that the terms are arranged in descending order of their degree. This format makes it easier to analyze and understand the polynomial's behavior. For example, after performing the multiplication and combining like terms, the resulting polynomial should be expressed in standard form, such as ax^n + bx^(n-1) + ... + c.